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Study Guides > ALGEBRA / TRIG I

Introduction to Applying Exponent Rules

What you'll learn to do: Simplify expressions using properties of exponents

In this section we will learn how to simplify and perform mathematical operations such as multiplication and division on terms that have exponents. We will also learn how to use scientific notation to represent very large or very small numbers, and perform mathematical operations on them. Specifically, in this section you’ll learn how to:
  • Evaluate exponential expressions
  • Simplify expressions using the Product Property of Exponents
  • Simplify expressions using the Power Rule of Exponents
  • Simplify expressions using the Product to a Power Property
  • Simplify expressions using the Quotient Properties of Exponents
  • Simplify exponential expressions containing negative exponents and exponents of 0 and 1
  • Simplify complex expressions using a combination of exponent rules
  • Simplify compound expressions using a combination of exponent rules
  Before you get started, take this readiness quiz.

Readiness Quiz

1) [ohm_question]144737[/ohm_question] If you missed this problem, review the following video. https://youtu.be/HkPGTmAmg_s 2) [ohm_question]144745[/ohm_question] If you missed the problem, review the example below.
Simplify: [latex]{3}^{4}[/latex]

Answer: Solution

[latex]{3}^{4}[/latex]
Expand the expression. [latex]3\cdot 3\cdot 3\cdot 3[/latex]
Multiply left to right. [latex]9\cdot 3\cdot 3[/latex]
[latex]27\cdot 3[/latex]
Multiply. [latex]81[/latex]

3) [ohm_question]145337[/ohm_question] If you missed the problem, review this video. https://youtu.be/qB5PZzmjenI 4) [ohm_question]130[/ohm_question] If you missed this problem, review this video. https://youtu.be/0-4rLGvVEOI 5) [ohm_question]146568[/ohm_question] If you missed this problem, review the video below. https://youtu.be/aLsWWl2-aNE 6) [ohm_question]145195[/ohm_question] If you missed this problem, review the following example.
Simplify: [latex-display]-7-\left(-4\right)\text{ and }-7+4[/latex-display]

Answer: Solution:

[latex]-7-\left(-4\right)[/latex] and [latex]-7+4[/latex]
Subtract to simplify. [latex]-7-\left(-4\right)=-3[/latex]
Add to simplify. [latex]-7+4=-3[/latex]
Subtracting [latex]−4[/latex] from [latex]−7[/latex] is the same as adding [latex]4[/latex] to [latex]−7[/latex].

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Licenses & Attributions

CC licensed content, Shared previously

  • Ex: Evaluating Negative Numbers Raised to Powers. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
  • Example: Write Repeated Multiplication in Exponential Form. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
  • Question ID: 144737, 144745, 145337. Authored by: Lumen Learning. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.

CC licensed content, Specific attribution